This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ould consist of the bit pattern ½¼½ followed by one hundred ¼’s. Instead, we would like to represent numbers in a form Ü ¢ ¾Ý by giving the values of Ü and Ý . The IEEE ﬂoating point standard represents a number in a form Î ´ ¢Å ¢
× ¾ : ), where the interpre- ¯ ¯ ¯ ¯ ¯ ¯ The sign × determines whether the number is negative (× ½) or positive (× tation of the sign bit for numeric value 0 is handled as a special case. ¼ The signiﬁcand Å is a fractional binary number that ranges either between ½ and ¾ ¯ or between ¼ and ½ ¯. The exponent weights the value by a (possibly negative) power of two. The bit representation of a ﬂoating-point number is divided into three ﬁelds to encode these values: The single sign bit s directly encodes the sign ×. The -bit exponent ﬁeld exp The Ò-bit fraction ﬁeld frac Ò ½ ¡ ¡ ¡ ½ ¼ encodes the signiﬁcand Å , but the value encoded also depends on whether or not the exponent ﬁeld equals 0. ½ ¡ ¡ ¡ ½¼...
View Full Document